Adding and Subtracting Rational Expressions external image insert_table.gif

Standard & Assessment Anchor
M11.D.2.2.3 Simplify algebraic fractions.
Objective
We will add and subtract rational expressions and simplify complex fractions.


Add or subtract. Identify any x-values for which the expression is undefined

external image gif.latex?%5Cfrac%7Bx-3%7D%7Bx+4%7D+%5Cfrac%7Bx-2%7D%7Bx+4%7D

external image gif.latex?%5Cfrac%7Bx-3+x-2%7D%7Bx+4%7D
Add the numerators
external image gif.latex?%5Cfrac%7B2x-5%7D%7Bx+4%7D
Combine like terms

The expression is undefined at x = -4 since the denominator will be equal to 0 at this value of x.



If we have unlike denominators, we have to multiply both numerator and denominator by a factor with an equivalence of 1 that will result in common denominators.

We will probably have to factor the denominators to determine what we must multiply by to result in a common denominator. We also have to remember to identify any values of x that make the expression undefinefd -- that is, division by 0.
Our first step is to find the least common multiple for each pair of factors. It might be a monomial, but it might also be a polynomial.



Find the least common multiple for the pair:

If we factor the trinomials, we can write




external image gif.latex?x%5E%7B2%7D-2x-3%5C:&space;%5C:&space;and%5C:&space;x%5E%7B2%7D-x-6